In a ΔABC, AD is

(a) In right triangle ALC

Using Pythagoras theorem, we have

AC² = AL² + LC²

⇒ AC² = AD² − DL² + (DL + DC) ²

….(1)

(b) In right triangle ALD

Using Pythagoras theorem, we have

AL² = AD² - LD²

Again, in ΔABL

Using Pythagoras theorem, we have

AB² = AL² + LB²

⇒ AB² = AD² –DL² + LB²

⇒ AB² = AD²–DL² + (BD – DL)²

……(2)

(c) Adding (1) and (2)